This paper is motivated by the empirical regularity that industries differ greatly in the level of firm turnover, and that entry and exit rates are positively correlated across industries. Our objective is to investigate the effect of sunk costs and, in particular, market size on entry and exit rates, and hence on the age distribution of firms. We analyze a stochastic dynamic model of a monopolistically competitive industry. Each firm's efficiency is assumed to follow a Markov process. We show existence and uniqueness of a stationary equilibrium with simultaneous entry and exit: efficient firms survive while inefficient ones leave the market and are replaced by new entrants. We perform comparative dynamics with respect to the level of sunk costs: entry costs are negatively and fixed production costs positively related to entry and exit rates. A central empirical prediction of the model is that the level of firm turnover is increasing in market size. The intuition is as follows. In larger markets, price-cost margins are smaller since the number of active firms is larger. This implies that the marginal surviving firm has to be more efficient than in smaller markets. Hence, in larger markets, the expected life span of firms is shorter, and the age distribution of firms is first-order stochastically dominated by that in smaller markets. In an extension of the model with time-varying market size, we explore the comovements between market size and entry and exit rates. It is shown that both entry and exit rates tend to rise over time in growing markets. In the empirical part, the prediction on market size and firm turnover is tested on industries where firms compete in well-defined geographical markets of different sizes. Using data on hair salons in Sweden, we show that an increase in market size or fixed costs shifts the age distribution of firms towards younger firms, as predicted by the model.